The Geometry of Packing
Rolling vs. Folding: An Interactive Essay
1. Intuition vs. Reality
When packing for a trip, the eternal debate is Folding vs. Rolling. Intuition suggests that rolling clothes compresses them, saving massive amounts of space. But is that true?
Surprising? In controlled experiments, both methods consume the exact same volume. A cotton fiber is a solid; you can't change its volume just by bending it differently. However, that doesn't mean the methods are equal.
2. Conservation of Volume
A t-shirt is a deformable solid. Whether you fold it into a rectangle or roll it into a cylinder, the amount of fabric remains constant. The only variable that changes volume is Air.
3. The Bin Packing Problem
If volume is conserved, why do travelers prefer rolling? It solves the Bin Packing Problem. Suitcases aren't perfect rectangles—they have wheel wells and handle ridges. Large rigid shapes (folded clothes) waste space in corners.
4. The Algorithm of Time
The most significant difference found in the experiment wasn't space, but Time. Rolling is a simpler algorithm to execute with fewer steps (Fold half, Roll fast) versus Folding (Align seams, flatten, fold, fold, smooth).
5. The Exception
Algorithms have edge cases. The video notes one major exception: The Collared Shirt. Rolling applies stress to the fabric structure.